Faculty Advisor

Tilley, Burt S.


The purpose of this project was to mathematically model a Slinky-Coil Geothermal Heating System. We first consider and discuss the difficulties of modeling one loop of a slinky coil. We then reduce the problem further to analyzing a half-loop, through non-dimensionalization, separation of variables, eigenfunction expansions, and perturbation series to obtain a function to model the temperature of the slinky coil. In both cases, we examine the quasi-steady approximation, which gives us a steady-state solution to our problem. Our model can successfully model the temperature rise, but it is very inefficient as it requires a very large amount of loops, on the order of thousands, to sustain the ambient temperature of the soil.


Worcester Polytechnic Institute

Date Accepted

May 2015


Mathematical Sciences

Project Type

Major Qualifying Project



Advisor Department

Mathematical Sciences